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C17×ΓL(1,𝔽8)×C13⋊C3 #28358196

order13923
automorphism?
homologyAbelianization (H1) = C32×C17 · Schur multiplier (H2) = C3

Aliases

direct productC17×ΓL(1,𝔽8)×C13⋊C3
unambiguous semidirect product(C13×ΓL(1,𝔽8))⋊(C3×C17)
unambiguous semidirect product(C7×C13⋊C3)⋊(C3×C17)
unambiguous semidirect product#63270⋊(C3×C17)
unambiguous semidirect product#63271⋊(C3×C17)
unambiguous semidirect product(C7×C17×C13⋊C3)⋊C3
unambiguous semidirect product(C13×C17×ΓL(1,𝔽8))⋊C3
unambiguous semidirect product(C17×#63270)⋊C3
unambiguous semidirect product(C17×#63271)⋊C3

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C32
derived, HallC7×C13 ⋊ C32×C17
HallC13×C17 ⋊ C3×ΓL(1,𝔽8)
HallC7×C17 ⋊ C3×C13⋊C3
SylowC13 ⋊ C3×C17×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C17×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC17ΓL(1,𝔽8)×C13⋊C3
commutator, cosocle, hypocenterC7×C13C32×C17
FrattiniC1G
Fitting, socleC7×C13×C17C32
LCSG ▷ C7×C13
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1547

Conjugacy classes & character table

595 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC17×ΓL(1,𝔽8)⋊(D13⋊C3), C17⋊(ΓL(1,𝔽8)⋊(D13⋊C3)), C17×C13⋊C3×AGL(1,𝔽7), …
maximal normal subgroup ofC17×ΓL(1,𝔽8)⋊(D13⋊C3), C17⋊(ΓL(1,𝔽8)⋊(D13⋊C3)), C17×C13⋊C3×AGL(1,𝔽7), …
maximal quotient ofC2×C17×ΓL(1,𝔽8)×C13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13923, 7);